Modulating optical signals for PAM-N (pulse amplitude modulation to “N” levels) is generally performed using Mach-Zehnder (MZ) modulators with multi-segment phase shifters, or MZ-ring hybrid modulators. Such MZ modulators are large (about 1 mm) compared to other optical devices in high density photonic integrated circuits (PICs), resulting in PICs of lower density. While MZ assisted ring modulators are about an order of magnitude smaller (phase shifter length of 340 um), they are still large compared to other optical device in high density PICs. While some MZ coupled ring modulator designs have been demonstrated they have relatively slow speeds (e.g. about 120 Mb/s. Alternatively, single electrode modulators can be driven to different voltage levels using linear drivers, but these drivers require high power dissipation to achieve linear performance.